Electronic devices may be formed by patterning successive layers on a substrate using lithography. The patterns are formed using an imaging plate such as a mask or reticle that is designed to produce the desired features on the substrate. As device feature sizes decrease, more complex mask designs are used.
For example, masks incorporating phase shift technology (referred to as phase shift masks) may be used to pattern small features. In a non-phase shift mask, the light transmitted through adjacent features is in phase, so that between adjacent features the amplitude of the light adds together. In a phase shift mask, light transmitted through adjacent features may be phase shifted so that between the features the amplitude of the light from one feature is about equal to but opposite in sign to the amplitude of the light from the other feature. This destructive interference may allow greater control over the creation of small features.
Mask design may be performed using software. For complex mask designs (e.g., design of phase shift masks for sub-wavelength features), accurate mask design software may be undesirably slow. In contrast, faster mask design software may not be suitably accurate.
A number of different methods may be used by the software to design masks. For example, a method referred to as a thin mask method uses geometrical optics to calculate the transmitted field, ignoring light scattering effects due to mask features. A boundary layer method modifies the thin mask field in feature edge areas (the so-called boundary layer) to account for some scattering effects. The edge domain decomposition method adds edge scattering corrections to the thin mask field to improve the accuracy.
Like reference symbols in the various drawings indicate like elements.